Kenneth Hickey and W. Earle Waghorne* Department of Chemistry, University College Dublin, Belfield, Dublin 4, Ireland

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1 J. Chem. Eng. Data 2001, 46, Viscosities and Volumes of Dilute Solutions of Formamide in Water + Acetonitrile and for Formamide and N,N-Dimethylformamide in Methanol + Acetonitrile Mixed Solvents: Viscosity B-Coefficients, Activation Free Energies for Viscous Flow, and Partial Molar Volumes Kenneth Hickey and W. Earle Waghorne* Department of Chemistry, University College Dublin, Belfield, Dublin 4, Ireland The viscosity B-coefficients and partial molar volumes have been measured for N,N-dimethylformamide and formamide in methanol + acetonitrile solvent systems and for N,N-dimethylformamide in water + acetonitrile mixed solvents. These data are used to calculate the solute contribution to the activation free energy for viscous flow, µ * 13, for these systems. It is found that the µ * 13 values are simply related to the corresponding enthalpies of transfer. Introduction The measurement of the viscosities of solutions formed the basis of some of the earliest studies of solute-solvent interactions. Jones and Dole 1 showed that the viscosities of dilute solutions of strong electrolytes could be represented as η 13 /η 1 ) η r ) 1 + A c + Bc (1) where η 13 and η 1 are the viscosities of the solution and solvent, respectively, and c is the solute concentration. The A-coefficient takes account of ion-ion interactions and can be calculated 2 and the B-coefficient reflects the effects of solute-solvent interactions on the solution viscosity. The viscosities of dilute solutions of nonassociated nonelectrolytes can be similarly represented as η 13 /η 1 ) η r ) 1 + Bc (2) where the symbols have the obvious meanings. B-coefficients have been measured for a wide range of electrolytes in aqueous solutions and for a smaller number of electrolytes in organic and mixed aqueous-organic solvents. 3 Nonelectrolytes have been less extensively studied although data are available for several solutes in water 4,5 and for 2-methylpropan-2-ol (tert-butyl alcohol) in aqueous methanol solvent systems. 6 In the present paper we present viscosity B-coefficients and partial molar volumes for formamide and N,N-dimethylformamide in methanol + acetonitrile mixed solvents at and K and for N,N-dimethylformamide in water + acetonitrile solvents at and K. We also report viscosity and volume data for the solvent mixtures at these temperatures. The values of the solute contribution to the free energy of activation for viscous flow, µ * 13, were calculated from the B-coefficients and molar volumes using the Feakins 6,7 * To whom correspondence should be addressed. relationship. It is found that the µ * 13 values are simply related to the enthalpies of transfer of the solutes in the same solvent systems. Experimental Section Viscosity. The viscosity measurements were made using a Schott-Gerate AVS/S measuring system and an Ubbelohde type suspended level capillary viscometer as described previously. 8 The system was adapted to allow serial measurements to be made under computer control. The modification to the capillary viscometer involved replacing the lower reservoir by one with a volume of about 50 cm 3. The viscometer was suspended in a specially constructed double water bath, which allowed the contents of the reservoir to be stirred using a magnetic stirrer. The temperature of the inner bath was stable to (0.001 K and was within (0.01 K of the reported temperature. The composition of the solution in the viscometer was altered by the addition of a stock solution, via a piston driven buret (Metrohm Dosimat 655, using a1cm 3 buret), through the sidearm of the viscometer. The AVS was controlled and interrogated through its RS-232 port, and the stirrer and buret were activated using reed relays under computer control. Thus, in an experiment a known volume of solvent was placed in the viscometer and its flow time measured. Subsequently, known volumes of a stock solution were injected into the viscometer and mixed by stirring, and the flow times of the resulting solutions were measured. The weight of a 1 cm 3 injection of the stock solution was measured before and after the experiment, and the density of the final solution was measured as a check on the final solution concentration. Typically B-coefficients were determined from measurements at nine solute concentrations (to 0.12 mol dm -3 ). The precisions of the B-coefficients, expressed as standard errors, are listed in the tables. Density. Densities were measured using a vibrating tube densitometer (Anton Paar DMA-60) with two cells (DMA /je CCC: $ American Chemical Society Published on Web 05/11/2001

2 852 Journal of Chemical and Engineering Data, Vol. 46, No. 4, 2001 Table 1. Densities and Viscosities of Methanol (1) + x 2 gcm -3 mpa s x 2 gcm -3 mpa s g e h g i i b d c e d g g i h i f g g i i f g g i i a Precisions are ( in the densities and (0.2% in the viscosities; x 2 represents the acetonitrile b Ref 11. c Ref 12. d Ref 16. e Ref 18. f Ref 13. g Ref 14. h Ref 15. i Ref 17. Table 2. Densities and Viscosities of Water (1) + x 2 gcm -3 mpa s x 2 gcm -3 mpa s K a Precisions are ( in the densities and (0.2% in the viscosities except for pure water, where those for the densities are ( ; x 2 represents the acetonitrile 601) with one, containing water, used as reference. This configuration has the advantage of minimizing the effects of variations in temperature. The system was fitted with an automatic sampler unit (Anton Paar SP-2). The apparatus was enclosed in an air thermostat kept at 0.5 K above the measuring temperature so that outgassing of samples was minimized. The temperature of the cell was controlled by circulation of water from a double water bath, the circulating bath was stable to (0.003 K, and the measuring cell temperature was within (0.01 K of the reported temperature. Figure 1. Excess molar volumes at for (a) water (1) + acetonitrile (2) mixtures [ref 11 (4), ref 12 (0), and the present results (b)] and (b) methanol (1) + acetonitrile (2) mixtures [ref 14 (4), ref 15 (O), ref 17 (0), ref 18 (3), and the present results (b)]. Chemicals. N,N-Dimethylformamide, 9 formamide, 9 and acetonitrile 10 were purified as described previously. Water was distilled, passed through an ion exchange column, and then redistilled; the conductivity of the water was < Scm 2. Results The densities and viscosities of the mixed solvent systems are listed in Tables 1 and 2. The excess molar volumes of the mixed solvents are shown in Figure 1, and the corresponding viscosities are shown in Figure 2. Also shown in Figures 1 and 2 are comparable data taken from the literature In all cases the agreement among the data is excellent. We note that our viscosities for the methanol + acetonitrile system at are marginally but systematically lower than those of Saha et al. 14 and Nikam et al. 16 The densities of formamide and N,N-dimethylformamide solutions in the mixed solvents followed the Root equation: 19

3 Journal of Chemical and Engineering Data, Vol. 46, No. 4, Figure 3. B-coefficients of formamide in methanol (1) + acetonitrile (2) mixtures at (4) and (3), N,N-dimethylformamide in acetonitrile + methanol mixtures at (O) and (0), and N,N-dimethylformamide in water (1) + acetonitrile (2) mixtures at K (9) and (b). η 1 ) ( hn A Vh 1 o ) where N A and h are Avogadro s number and Planck s constant and the other symbols have the obvious meanings. For a solution containing a solute (3) dissolved in a pure liquid (1) they proposed η 13 ) ( hn A Vh 13 ) ( exp µ o* 1 ( exp Gh * 13 RT ) (5) RT ) (6) where Vh 13 and Gh * 13 are the mean molar volume and the average Gibbs energy of activation for viscous flow. In the case of dilute solutions we write Figure 2. Solvent viscosities for (a) water (1) + acetonitrile (2) mixtures [ref 16 (O), ref 18 (0), and the present results (b) at and the present results ([) at K] and (b) methanol (1) + acetonitrile (2) mixtures at and [ref 17 (O), ref 15 (4), ref 14 (0), ref 18 (3), and the present results (b)]. F 1,3 )F 1 + ac (3) to within experimental error, and the partial molar volumes, V φ, of the solutes were obtained from the values of R as R) (M 3 -F 1 V φ ) 1000 In eqs 3 and 4, c represents the solute concentration, F 1,3 and F 1 represent the densities of the solution and mixed solvent, and M 3 is the molecular weight of the solute. The viscosities of the formamide and N,N-dimethylformamide solutions followed eq 2. The partial molar volumes and B-coefficients for the systems studied are reported in Tables 3-5, and the B-coefficients are shown in Figure 3. Eyring and co-workers 20 proposed that the free energy of activation for viscous flow of a pure liquid (1), µ 1 o*, could be calculated via (4) Gh * 13 ) x 1 µ o* * 1 + x 3 µ 3 Feakins 6,7 showed that, if eqs 1 (or 2) and 7 are obeyed, then where the coefficient ν is one for an undissociated solute, as in the present work, and would be, for example, 2 for a fully dissociated univalent electrolyte. The activation free energies for the mixed solvents Gh * 1,2 were calculated from their viscosities, η 13, via eq 6 and are listed in Tables 6 and 7. The µ * 13 values calculated from the B-coefficients are listed in Tables 8 and 9 and are shown graphically in Figure 4. Discussion It is clear from Figure 4 that, with the exception of the values in pure water, the temperature variation of µ * 13 is close to the limit of its precision. Qualitatively this corresponds to a situation where the activation entropy is small and µ * 13 is dominated by the enthalpy of activation. These solute-solvent systems have been extensively studied by calorimetry 21,22 and infrared spectroscopy. 23,24 (7) B ) (νvh o 1 - V φ3 ) + ( Vh o 1 RT)( µ * 3 - ν µ o* 1 ) (8)

4 854 Journal of Chemical and Engineering Data, Vol. 46, No. 4, 2001 Table 3. Limiting Partial Molar Volumes and Viscosity B-Coefficients for N,N-Dimethylformamide (3) in Methanol (1) + x 2 V φ/cm 3 mol -1 B/dm 3 mol -1 x 2 V φ/cm 3 mol -1 B/dm 3 mol ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( a Precisions shown are the standard deviations; x 2 represents the acetonitrile Figure 4. Solute contributions to the activation chemical potential for viscous flow, µ 3 θ*, for N,N-dimethylformamide in water (1) + acetonitrile (2) mixtures at K (b) and (O) and methanol (1) + acetonitrile (2) mixtures at (9) and (0) and for formamide in methanol (1) + acetonitrile (2) mixtures at (2) and (4). In the present context the calorimetric studies are the more interesting. * In each of the systems considered the variation in µ 13 is similar to that in the corresponding enthalpy of transfer, t H θ, but is inverted and differs in magnitude. In effect we can write µ 3 θ* =-{A t H θ } (9) where µ * 13 is the change in µ * 13 and A is simply a proportionality constant. This is shown in Figure 5, which shows the t H θ and µ * 13 values for the three systems reported here as a function of solvent composition. Also shown in Figure 5 are Figure 5. Variation in the solute contribution to the activation chemical potential for viscous flow, µ 3 θ*, (open symbols) and enthalpies of transfer, th 3 θ, (filled symbols) for N,N-dimethylformamide in water (1) + acetonitrile (2) (4) and methanol (1) + acetonitrile (2) (O) mixtures and for formamide in methanol (1) + acetonitrile (2) mixtures (0); the line through the µ 3 θ* data corresponds to eq 9 (see text). lines corresponding to eq 9. In the methanol + acetonitrile system the µ * 13 values conform sensibly to eq 9 over the whole range of solvent compositions, while in the aqueous acetonitrile system there is a divergence at acetonitrile mole fractions above 0.8.

5 Table 4. Limiting Partial Molar Volumes and Viscosity B-Coefficients for Formamide (3) in Methanol (1) + Acetonitrile (2) Mixtures a x 2 V φ/cm 3 mol -1 B/dm 3 mol -1 x 2 V φ/cm 3 mol -1 B/dm 3 mol ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( a Precisions shown are the standard deviations; x 2 represents the acetonitrile Table 5. Limiting Partial Molar Volumes and Viscosity B-Coefficients for N,N-Dimethylformamide (3) in Water (1) + x 2 V φ/cm 3 mol -1 B/dm 3 mol -1 x 2 V φ/cm 3 mol -1 B/dm 3 mol K ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( a Precisions shown are the standard deviations; x 2 represents the acetonitrile Journal of Chemical and Engineering Data, Vol. 46, No. 4, Table 6. Molar Free Energies of Activation for Viscous Flow, Gh * 12, for Methanol (1) + Gh * 12 /kj mol -1 x a Precisions are (0.2 kj mol -1 ; x 2 represents the acetonitrile While eq 9 represents the µ * 13 data for the nonelectrolyte systems reported here, its wider applicability is not clear. There are not data available for other nonelectrolyte systems against which eq 9 could be tested. There are viscosity 16 and enthalpy 25 data for several electrolyte systems including KCl and (C 4 H 9 ) 4 NBr in aqueous acetonitrile mixtures and for CsCl in highly aqueous propan-1- ol + water solvents. 26 In the cases of KCl and (C 4 H 9 ) 4 NBr in aqueous acetonitrile the data do not conform even approximately to eq 9 while the CsCl data in the highly aqueous propan-1-ol-water solvents are in qualitative (but not quantitative) agreement with eq 9. In the cases reported here µ 3 θ* is dominated by the activation enthalpy and so eq 9 may reflect an underlying relationship between the transfer and activation enthalpies. Testing this requires B-coefficients (and molar volumes) at two or more temperatures as well as the corresponding transfer enthalpies. There are relatively few systems where this body of data is available; however, for CsCl in highly aqueous propan-1-ol mixtures the necessary data are available 26 and show no correlation between the transfer and activation enthalpies. It may then be that eq 9 is applicable to nonelectrolyte systems but not to those involving electrolytes, perhaps because the solvent-nonelectrolyte interactions are shorter range and significantly weaker than those with ionic solutes.

6 856 Journal of Chemical and Engineering Data, Vol. 46, No. 4, 2001 Table 7. Molar Free Energies of Activation for Viscous Flow, Gh * 12, for Water (1) + t and a Gh * 12/kJ mol -1 x K a Precisions are (0.2 kj mol -1 ; x 2 represents the acetonitrile Table 8. Solute Contribution to the Free Energy of Activation for Viscous Flow, µ 3 θ*, for N,N-Dimethylformamide and Formamide in Methanol (1) + µ 3 θ* /kj mol -1 N,N-dimethylformamide formamide x a Precisions are (0.2 kj mol -1 ; x 2 represents the acetonitrile Table 9. Solute Contribution to the Free Energy of Activation for Viscous Flow, µ θ* 3, for N,N-Dimethylformamide in Water (1) + Acetonitrile (2) Mixtures a µ3 θ* /kj mol -1 x K a Precisions are (0.2 kj mol -1 ; x 2 represents the acetonitrile Literature Cited (1) Jones, G.; Dole, M. The Viscosities of Aqueous Solutions of Strong Electrolytes with Special Reference to Barium Chloride. J. Am. Chem. Soc. 1929, 51, (2) Falkenhagen, H.; Dole, M. Die Innere Reibung von Elektrolytischen und ihre Deutung nach der Debeschen Theorie. Phys. Z. 1929, 30, (3) Jenkins, H. D. B.; Marcus, Y. Viscosity B-Coefficients of Ions in Solution. Chem. Rev. 1995, 95, (4) Rupley, J. A. The Effect of Urea and Amides on Water Structure J. Phys. Chem. 1964, 68, (5) Herkovits, T.; Kelly, T. M. Viscosity Studies of Aqueous Solutions of Alcohols, Ureas and Amides. J. Phys. Chem. 1973, 77, (6) Feakins, D.; Canning, F. M.; Waghorne, W. E.; Lawrence, K. G. Relative Viscosities and Quasi-thermodynamics of Solutions of tert-butyl Alcohol in the Methanol-Water System: A different View of the Alkyl-Water Interactions. J. Chem. Soc., Faraday Trans. 1993, 89, (7) Feakins, D.; Freemantle, D.; Lawrence, K. G. Transition State Treatment of the Relative Viscosity of Electrolyte Solutions. Application to Aqueous, Nonaqueous and Methanol + Water Systems. J. Chem. Soc., Faraday Trans , 70, (8) Crudden, J.; Delaney, G. M.; Feakins, D.; O Reilly, P. J.; Waghorne, W. E.; Lawrence, K. G. The Viscosity and Structure of Solutions. Part 2. Measurement of the B-Coefficient of Viscosity for Alkali-metal Chlorides in Propan-1-ol-Water-Electrolyte Mixtures at 25 and 35 C. J. Chem. Soc., Faraday Trans , 13, (9) Feakins, D.; O Duinn, C.; Waghorne, W. E. Enthalpies of Transfer of N-Methylformamide, Formamide and N,N-Dimethylformamide from Methanol to Methanol + Dimethylsulphoxide Mixtures. J. Solution Chem. 1987, 16, (10) Cox, B. G.; Waghorne, W. E. Free Energies, Enthalpies and Entropies of Transfer of Electrolytes from Propylene Carbonate to Dimethylsulphoxide + Propylene Carbonate Mixtures and from Methanol to Acetonitrile + Methanol Mixtures at 25 C. J. Chem. Soc., Faraday Trans , 80, (11) Handa, Y. P.; Benson, G. C. Thermodynamics of Aqueous Mixtures of Nonelectrolytes. IV. Excess Volumes of Water-Acetonitrile Mixtures from 15 to 35 C. J. Solution Chem. 1981, 10, (12) van Meurs, N.; Somsen, G. Excess and Apparent Molar Volumes of Mixing of Water and Acetonitrile between 0 and 25 C. J. Solution Chem. 1993, 22, (13) Sandhu, J. S.; Sharma, A. K.; Wadi, R. K. Excess Molar Volumes of 1-Alkanol (C 1-C 5) Binary Mixtures with Acetonirile. J. Chem. Eng. Data 1986, 31, (14) Saha, N.; Das, B.; Hazra, D. K. Viscosities and Excess Molar Volumes for Acetonitrile + Methanol at , and K. J. Chem. Eng. Data 1995, 40, (15) Bakshi, M. S.; Singh, J.; Kaur, H.; Ahmed, S. T.; Kaur, G. Thermodynamic Behaviour of Mixtures. 3. Mixtures of Acetonitrile with Dimethylacetamide, Dimethyl Sulfoxide, Nitrobenzene and Methanol at 25 C. J. Chem. Eng. Data 1996, 41, (16) Nikam, P. S.; Sawant, A. B. Viscosity of Potassium Halides and Symmetrical Tetraalkylammonium Halides in Acetonitrile + Water Mixtures at. J. Chem. Eng. Data 1997, 42, (17) Nikam, P. S.; Shirsat, L. N.; Hasan, M. Density and Viscosity Studies of Binary Mixtures of Acetonitrile with Methanol, Ethanol, Propan-1-ol, Propan-2-ol, Butan-1-ol, 2-Methylpropan-1-ol and 2-Methylpropan-2-ol at (298.15, , and ) K. J. Chem. Eng. Data 1998, 43, (18) Cunningham, G. P.; Vidulich, G. A.; Kay, R. L. Several Properties of Acetonitrile-Water, Acetonitrile-Methanol and Ethylene Carbonate-Water Systems. J. Chem. Eng. Data 1967, 12, (19) Root, W. C. An Equation Relating Density and Concentration. J. Am. Chem. Soc. 1933, 55, (20) Glasstone, S.; Laidler, K. J.; Eyring, H. The Theory of Rate Processes; McGraw-Hill: New York, 1941; p 480. (21) Costigan, A.; Feakins, D.; McStravick, I.; O Duinn, C.; Ryan, J.; Waghorne, W. E. Enthalpies of Transfer of some Nonelectrolytes from Acetonitrile to Acetonitrile-Methanol Mixtures. J. Chem. Soc., Faraday Trans. 1991, 87, (22) Feakins, D.; Hogan, P.; O Duinn, C.; Waghorne, W. E. Enthalpies of Transfer of Formamide, N-Methylformamide, and N,N-Dimethylformamide from Water to Aqueous Acetonitrile Mixtures at 298 K. J. Chem. Soc., Faraday Trans. 1992, 88, (23) Eaton, G.; O Duinn, C.; Rastogi, P. P.; Symons, M. C. R.; Waghorne, W. E. Solvation of Some Amides in Mixed Solvent Systems. Comparison of the Results of Infra-Red Spectroscopic and Calorimetric Measurements. J. Chem. Soc., Faraday Trans. 1992, 88, (24) Meade, M.; Hickey, K.; McCarthy, Y.; Rastogi, P. P.; Symons, M. C. R.; Waghorne, W. E. The Solvation of Some Non-Electrolytes in the Methanol + Acetonitrile Solvent System. A Combined

7 Journal of Chemical and Engineering Data, Vol. 46, No. 4, Calorimetric and Spectroscopic Study. J. Chem. Soc., Faraday Trans. 1997, 93, (and references therein). (25) Cox, B. G.; Natarajan, R.; Waghorne, W. E. Thermodynamic Properties for Transfer of Electrolytes from Water to Acetonitrile and to Acetonitrile + Water Mixtures. J. Chem. Soc., Faraday Trans , 75, (26) Crudden, J.; Delaney, G. M.; Feakins, D.; O Reilly, P. J.; Waghorne, W. E.; Lawrence, K. G. The Viscosity and Structure of Solutions. Part 3. Interpretation of the Thermodynamic Activation Parameters for Propan-1-ol-Water-Electrolyte Systems. J. Chem. Soc., Faraday Trans , 82, Received for review November 29, Accepted March 19, JE

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